We study constraint satisfaction problems on the domain {-1, 1}, where the given constraints are homogeneous linear threshold predicates. That is, predicates of the form sgn(w1x1 +...
A predicate P : {−1, 1}k → {0, 1} can be associated with a constraint satisfaction problem Max CSP(P). P is called “approximation resistant” if Max CSP(P) cannot be approxi...
We prove two main results on how arbitrary linear threshold functions f(x) = sign(w · x − θ) over the n-dimensional Boolean hypercube can be approximated by simple threshold f...
We consider the problem of learning in multilayer feed-forward networks of linear threshold units. We show that the Vapnik-Chervonenkis dimension of the class of functions that ca...